It is proposed to use ZF and TF muSR to study the low temperature, low field part of the phase diagram of Ba3CuSb2O9, a system with a uniform triangular lattice of S=1/2 Cu ions that is believed to provide an example of a triangular lattice quantum spin liquid. Measurements will be made in a similar manner to those recently reported by us in the 31st March issue of Nature for a molecular dimer based quantum spin liquid system. Comparison of the properties of this Cu-based spin system with those of the molecular radical based system will be most valuable for progressing the understanding of the intriguing quantum spin liquid phases of all these materials.